IPS - After Tax Nominal Rate of Return

From Finquiz

Don’t understand how they got the required after tax nominal rate of return (answer below question)

Jorge Andres is an electrical engineer in the city of Medellin, Colombia. He hopes to retire next year at the age of 60 and visit friends in the United States and Europe. When he retires, he will receive a one-time, taxable payment of COP250 million from his employer’s pension fund and he will start receiving COP15 million from an annuity. The annuity will continue each year throughout his retirement with the proceeds growing at the rate of inflation and taxed as capital gains. His current after-tax salary of COP24 million fully covers living expenses.

Jorge Andres will also sell COP20 million of company stock that he has accumulated with an original basis of COP5 million. He is not married but has a son that will be entering a four-year college next year. He would like to help his son pay tuition but has talked about capping the amount he will pay at COP5 million per year. Tuition fees have been increasing at a rate of 5% so Jorge agreed to increase the amount each year by that amount.

Jorge currently has a portfolio of COP450 million with an allocation to 40% government bonds, 40% corporate bonds and 20% stocks, on which he earns 4% in interest and dividends and is estimated to grow by 3% per year. He estimates that his living expenses will increase by the general rate of inflation in Colombia of 5% each year. He owns his home, valued at COP210 million but would like to keep it separate from the rest of his plans and pass it to his son through the estate. He would like to maintain the value of his retirement assets.

Jorge Andres pays 25% taxes on income and dividends. There are no taxes on capital gains as long as the seller makes less than COP45 million per year. He is talking with his financial advisor, Joseph Hogue, to prepare an IPS and talk about next year. During the interview, Jorge mentions that he has lost money in investments before and is reluctant to put too much risk in his portfolio. He has worked hard to build for his retirement and he does not want to jeopardize it. In order to maintain his asset value, he is willing to reduce expenses in retirement.


They calculated a required return of 7.4% In the process they did some things that really confused me.

Specifically they did not remove the $20 million of company stock that they sold from his investment portfolio. They treated it as separate from the portfolio.

Also, for the income calc, they only included interest income from 1 year of $18mm. Why not in the 2nd year (first year of retirement)?

They answer also didnt include 3% growth in the portfolio in year two. Shoudlnt this be included to calculate the asset base for the return requirement?

Lastly, why is the $5mm college expense deducted from income rather than the asset base. Everything I have seen treats these large non-ongoing expenses (like mortgage payment) as deduction from asset base but not income. This did the opposite. Is it because its semi ongoing since its 4 years of expenses?


What is the calculation that gets to 7.4%? I’m having trouble getting there too.

I jsut did another IPS question by them. Even stupider. Finquiz kinda sucks. Bought the test for additional materials but I keep finding weird issues.

Ive actually worked out some of the issues with this queston. Howecer, still doesnt make sense to me why the interest income ifor year 2 isnt included.